Many industries have an interest in mapping values for a particular quantity over an area of interest. Such maps may aid in performing tasks associated with the industry. For example, maps showing water depths are important in maritime shipping and navigation. Contour maps showing land elevations may be used in planning communities, building roads, constructing reservoirs, etc. In the oil and gas exploration industry, maps showing the locations of oil deposits can help in deciding where and whether to initiate a drilling project. Maps of soil contamination levels can be used in clean up or treatment efforts.
The accuracy of such maps over an area of interest can be crucial. For example, in the oil and gas exploration industry, reliance on a map inaccurately suggesting the presence of oil and gas deposits may have significant negative consequences. All costs associated with equipment, personnel, and operations would be lost if drilling operations were established at a location mapped as having high oil concentration levels only to later discover through drilling that little oil was present at that location. Similar economic consequences may be realized in other industries that depend on mapped data.
In certain situations, creating accurate maps can be challenging. For some quantities, such as elevation, temperature, etc., measurement of particular values over an entire area of interest may be readily ascertainable using scanning measurement equipment to generate contour maps. Even in these situations, however, obtaining a desired level of precision in the measured data and in the coverage of data over the area of interest may be complex. In other cases, it may be difficult or impossible with known techniques to obtain a data scan over an entire area of interest. For example, oil or gas deposits may reside within stone layers or formations located deep below the Earth's surface. Determining the thickness of these stone layers may require drilling in several finite locations to determine the particular thickness values for the stone layer at those locations. Often it may be possible or practical to obtain measurements at a relatively small number of sample sites within an area of interest. As a result, data relating to a particular quantity of interest may be available for only a finite number of sample locations within the area of interest.
Generating a contour map of a particular quantity over an area of interest requires data corresponding to the values for that quantity over the area of interest. Where measured data is available for only a finite set of locations within the area of interest, a process of data extrapolation or projection is required to obtain calculated (estimated) data values to fill in the gaps between locations corresponding to the measured values. Various gridding techniques and extrapolation or estimation algorithms may be employed to calculate data values to supplement measured data within an area of interest. Often, such techniques involve averaging techniques to calculate predicted data values in the areas surrounding the measured values.
In addition to contour maps showing the measured and predicted data values over an area of interest, similar maps may be generated to map probabilities associated with the measured and predicted data values. For example, such probability maps may provide contours of percentages. In some cases, the percentages may be indicative of the likelihood that a particular quantity exceeds a certain value within the area of interest. Returning to the oil and gas example, a probability map may indicate over the area of interest the probability that a sub-surface oil-containing formation has a thickness greater than a predetermined value (e.g., 10 feet or any other thickness of interest).
While such probability maps can be useful in decision making (e.g., deciding where and whether to establish an oil or gas drilling operation), the current methods of generating such probability maps have several drawbacks that can lead to probability maps that have much higher levels of uncertainty than the mapped probabilities suggest. For example, any single map (or grid) generated using a specific gridding algorithm and a specific set of input parameters may look different (sometimes substantially different) from other maps generated with either different algorithms and/or different input parameters. Other than empirical measurement for all points on the map, there is no way to determine which of the generated maps is correct. In fact, none of the generated maps is likely correct, as each merely represents a single possibility. Only by generating a statistically significant number of maps with a statistically reasonable range of parameters can one arrive at a statistically valid interpolation between known data points.
Second, many known techniques for generating probability and statistical maps are based on locally calculated statistics which are then mapped. To the extent that many (if not all) gridding and mapping algorithms constitute some form of averaging tool, such an approach can be mathematically flawed, as average probabilities generated from averaged values would involve taking an average of a set of averages and/or a standard deviation of a set of standard deviations. There is a need for methods and systems for generating more robust probability maps.